No, it doesn't. It will drive off after a few corners. What he meant was that for a given dirt amount, the tyre will always have grip X, instead of X varying a bit/being random (I think).
Though I will not confirm that it really is like that, as we actually don't know for sure. Not too long ago we also thought that LFS doesn't model tyre surface temperature, which turned out to be wrong.
E: LOL, three different interpretations of the same sentence.
E2: By the way, at least according to the F9 menu, if you clip a dirty area the whole *width* of the tyre is affected, but not the whole circumference!